Block maps and Fourier analysis

Chunlan Jiang Department of Mathematics, Hebei Normal University, Shijiazhuang 050024, China Zhengwei Liu Department of Physics and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Jinsong Wu Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China

Spectral Theory and Operator Algebra mathscidoc:2207.32001

Science China Mathematics, 62, (8), 1585, 2019.7
We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For the \mathbb{Z}_2 case, the asymptotic phenomenon of the block map coincides with that of the 2D Ising model.The study of block maps requires a further development of our recent work on the Fourier analysis of subfactors.We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young's inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.
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  title={Block maps and Fourier analysis},
  author={Chunlan Jiang, Zhengwei Liu, and Jinsong Wu},
  booktitle={Science China Mathematics},
Chunlan Jiang, Zhengwei Liu, and Jinsong Wu. Block maps and Fourier analysis. 2019. Vol. 62. In Science China Mathematics. pp.1585.
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